Harmonic Centrality

The Harmonic Centrality algorithm calculates the harmonic centrality of each vertex in the graph. Harmonic Centrality is a variant of Closeness Centrality. In a (not necessarily connected) graph, the harmonic centrality reverses the sum and reciprocal operations in the definition of closeness centrality:

$$H(x)=\sum _{y\neq x}{\frac {1}{d(x,y)}}$$

If your graph has many unconnected clusters, the harmonic centrality could be a better indicator of centrality than closeness centrality.

For more information, see Harmonic Centrality.

Specifications

CREATE QUERY harmonic_cent(SET<STRING> v_type, SET<STRING> e_type, 
SET<STRING> re_type,INT max_hops=10, INT top_k=100, BOOL wf = TRUE, 
BOOL print_accum = True, STRING result_attr = "", STRING file_path = "", 
BOOL display_edges = FALSE)

Parameters

Name	Description	Data type
v_type	Vertex types to calculate harmonic centrality for	SET<STRING>
e_type	Edge types to traverse	SET<STRING>
re_type	Reverse edge types. For undirected edges, fill in the edge type name in this parameter as well as the e_type parameter.	SET<STRING>
max_hops	The maximum number of hops the algorithm would consider for each vertex. If set to a non-positive value, the limit is ignored.	INT
top_k	Sort the scores high to low and output the highest k scores	INT
wf	If true, use the Wasserman-Faust normalization for multi-component graphs	BOOL
print_accum	If true, output JSON to standard output	BOOL
result_attr	If not empty, store centrality values (FLOAT) to this attribute	STRING
file_path	If not empty, write output to this file in CSV.	STRING
display_edges	If true, include the graph's edges in the JSON output, so that the full graph can be displayed.	BOOL

Example

If we have the following graph, we can see that Ivy is the most central of the five vertices. Running the algorithm on the graph shows that Ivy has the highest centrality score:

GSQL Command

RUN QUERY harmonic_cent(["Person"], ["Coworker"], ["Coworker"], 4, 5, 
true, true, _, _, _)

Results

{
  "error": false,
  "message": "",
  "version": {
    "schema": 0,
    "edition": "enterprise",
    "api": "v2"
  },
  "results": [{"top_scores": [
    {
      "score": 0.04167,
      "Vertex_ID": "Ivy"
    },
    {
      "score": 0.03571,
      "Vertex_ID": "Damon"
    },
    {
      "score": 0.03571,
      "Vertex_ID": "George"
    },
    {
      "score": 0.025,
      "Vertex_ID": "Steven"
    },
    {
      "score": 0.025,
      "Vertex_ID": "Glinda"
    }
  ]}]
}

Visualized results